The show opened in Manchester on May 9 and 10 and was due to travel to Dublin, Belfast and Newcastle later in the month.
According to The Stage, an email from co-producer John Ward sent to the cast and crew said that he and his team were "far from happy with the show artistically" and were "not prepared to take it out again in its present form".
"We will be re-working the show for dates later in the year," the email continued.
"The upside is that we had a terrific reaction from the fans on both Wednesday and Thursday night and an improved show certainly has the potential to go on and be a long-running hit.
"We had some mixed reviews but also some raves. But it needs to be changed."
Directed by John Stephenson and choreographed by Stephen Mear and Karen Bruce, Street of Dreams stars Paul O'Grady and Jodie Prenger.
Its planned tour dates were The O2 Dublin (May 18 and May 19), Belfast's Odyssey Arena (May 21 and May 22) and Newcastle's Metro Radio Arena (May 29 and May 30). There has been no indication as to when these dates will be rescheduled.